A330137 Numbers m such that 1 < gcd(m, 30) < m and m does not divide 30^e for e >= 0.

14, 21, 22, 26, 28, 33, 34, 35, 38, 39, 42, 44, 46, 51, 52, 55, 56, 57, 58, 62, 63, 65, 66, 68, 69, 70, 74, 76, 78, 82, 84, 85, 86, 87, 88, 92, 93, 94, 95, 98, 99, 102, 104, 105, 106, 110, 111, 112, 114, 115, 116, 117, 118, 122, 123, 124, 126, 129, 130, 132, 134

Offset: 1

Author

Michael De Vlieger, Dec 02 2019

Keywords

• nonn
• easy

Comments

Numbers m that are neither 5-smooth nor reduced residues mod 30. Such numbers m have at least 1 prime factor p <= 5 and at least 1 prime factor q > 5.

Complement of the union of A007775 and A051037.

Analogous to A105115 for A120944(2) = 10. This sequence applies to the second primorial in A120944, i.e., 30 = A002110(2).

Examples

			14 is in the sequence since gcd(14, 30) = 2 and 14 does not divide 30^e with integer e >= 0.
15 is not in the sequence since 15 | 30.
16 is not in the sequence since 16 | 30^4.
17 is not in the sequence since 17 is coprime to 30.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A007775, A051037, A105115, A120944, A306999, A307589, A316991, A316992, A330136.

Programs

Mathematica

With[{nn = 135, k = 30}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]]